Why Do We Need Weight Decay in Modern Deep Learning?
read the original abstract
Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role remains poorly understood for deep learning. In this work, we highlight that the role of weight decay in modern deep learning is different from its regularization effect studied in classical learning theory. For deep networks on vision tasks trained with multipass SGD, we show how weight decay modifies the optimization dynamics enhancing the ever-present implicit regularization of SGD via the loss stabilization mechanism. In contrast, for large language models trained with nearly one-epoch training, we describe how weight decay balances the bias-variance tradeoff in stochastic optimization leading to lower training loss and improved training stability. Overall, we present a unifying perspective from ResNets on vision tasks to LLMs: weight decay is never useful as an explicit regularizer but instead changes the training dynamics in a desirable way. The code is available at https://github.com/tml-epfl/why-weight-decay
This paper has not been read by Pith yet.
Forward citations
Cited by 10 Pith papers
-
GQA-{\mu}P: The maximal parameterization update for grouped query attention
Derives μP scalings for GQA via promoted spectral-norm definition of feature learning and a modified norm preserving scaling laws for non-full-rank matrices, with experiments showing learning-rate transfer.
-
First-Passage Prediction of Grokking Delay: ACalibrated Law under AdamW with Causal Validation
A first-passage time model produces the law T_grok - T_mem = (1 / 2 kappa_LL eta lambda) log(V_mem / V_star) that predicts grokking delays with 17.7% MAPE on held-out AdamW runs after calibrating two parameters on one cell.
-
Training Deep Learning Models with Norm-Constrained LMOs
Scion is a new stochastic LMO-based optimizer family that unifies existing methods, supports unconstrained problems, and delivers hyperparameter transferability plus speedups on nanoGPT training.
-
Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
MD Decoupling factorizes weights into fixed-norm directions and learnable per-row/column magnitudes updated at independent rates, improving Adam and Muon training stability and scale transfer without weight decay or warmup.
-
Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics
Weight decay controls distinct learning regimes in grokking transformers on modular arithmetic, tracked by new cheap attention-based diagnostics with empirical critical value and exponent fits.
-
OUIDecay: Adaptive Layer-wise Weight Decay for CNNs Using Online Activation Patterns
OUIDecay adaptively rescales layer-wise weight decay in CNNs using an online activation-based Overfitting-Underfitting Indicator and outperforms fixed decay in 7 of 8 tested settings.
-
Demystifying Manifold Constraints in LLM Pre-training
Manifold constraints via the new MACRO optimizer independently bound activation scales and enforce rotational equilibrium in LLM pre-training, subsuming RMS normalization and decoupled weight decay while delivering co...
-
Anytime Training with Schedule-Free Spectral Optimization
SF-NorMuon is a new schedule-free spectral optimizer that closes the gap with tuned AdamW on 125M-772M parameter models across 1-8x Chinchilla horizons while providing stationarity guarantees.
-
When Does Removing LayerNorm Help? Activation Bounding as a Regime-Dependent Implicit Regularizer
DyT improves validation loss 27% at 64M params/1M tokens but worsens it 19% at 118M tokens, with saturation levels predicting the sign of the effect.
-
Gated Delta Networks: Improving Mamba2 with Delta Rule
Gated DeltaNet integrates gating and delta rules into linear transformers, outperforming Mamba2 and DeltaNet on language modeling, reasoning, retrieval, and long-context tasks.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.